Base-p-cyclic reduction for tridiagonal systems of equations

doi:10.1016/0168-9274(91)90046-3

Applied Numerical Mathematics

Volume 8, Issue 2, September 1991, Pages 117-125

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Abstract

Cyclic reduction is often heralded as a vectorizable and fast method for the solution of weakly diagonally dominant tridiagonal systems of equations on a vector processor. However, in the standard version, where the number of equations is halved in each sweep (recursive doubling), sooner or later the algorithm runs into memory bank conflicts because the stride in the memory access is doubled in each sweep and eventually becomes a multiple of the number of memory banks. In this note we consider variants of the algorithm, in which the stride is tripled after each sweep and/or the reduced system of equations is moved to contoguous locations beyond the original ones. We shall compare performances on CRAY X-MP and NEC SX-2 machines.

References (5)

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Divide and conquer: a new parallel algorithm for the solution of a tridiagonal linear system of equations
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N.J. Higham
Bounding the error in Gaussian elimination for tridiagonal systems
SIAM J. Matrix Anal. Appl.
(1990)

There are more references available in the full text version of this article.

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Base-p-cyclic reduction for tridiagonal systems of equations

Abstract

Divide and conquer: a new parallel algorithm for the solution of a tridiagonal linear system of equations

Bounding the error in Gaussian elimination for tridiagonal systems

SIAM J. Matrix Anal. Appl.